Characterization of Magnetoresistive Shunts and Its Sensitivity Temperature Compensation

The main purpose of the paper is to show how a magnetoresistive (MR) element can work as a current sensor instead of using a Wheatstone bridge composed by four MR elements, defining the concept of a magnetoresistive shunt (MR-shunt). This concept is reached by considering that once the MR element is biased at a constant current, the voltage drop between its terminals offers information, by the MR effect, of the current to be measured, as happens in a conventional shunt resistor. However, an MR-shunt has the advantage of being a non-dissipative shunt since the current of interest does not circulate through the material, preventing its self-heating. Moreover, it provides galvanic isolation. First, we propose an electronic circuitry enabling the utilization of the available MR sensors integrated into a Wheatstone bridge as sensing elements (MR-shunt). This circuitry allows independent characterization of each of the four elements of the bridge. An independently implemented MR element is also analyzed. Secondly, we propose an electronic conditioning circuit for the MR-shunt, which allows both the bridge-integrated element and the single element to function as current sensors in a similar way to the sensing bridge. Third, the thermal variation in the sensitivity of the MR-shunt, and its temperature coefficient, are obtained. An electronic interface is proposed and analyzed for thermal drift compensation of the MR-shunt current sensitivity. With this hardware compensation, temperature coefficients are experimentally reduced from 0.348%/°C without compensation to −0.008%/°C with compensation for an element integrated in a sensor bridge and from 0.474%/°C to −0.0007%/°C for the single element.


Introduction
Current sensing is required in many power electronic applications for control, power management, overcurrent protection, or monitoring tasks [1,2].Techniques used in measuring electric current include, mainly: shunt resistors, current transformers, Rogowski coils, Hall effect sensors, and magnetoresistive (MR) sensors [3].Shunt resistor-based techniques use an external resistor to measure current, which is dissipative and does not provide galvanic isolation [1,4].Current transformers use a magnetic core with a large number of secondary turns, the primary being winding the conductor through which the current to be measured circulates.This solution inherently provides galvanic isolation, but it requires large cores for low-frequency currents and precludes the measurement of DC currents [4,5].The Rogowski probe is a flexible coil, without a magnetic core, used to measure AC currents in high-power systems, providing accurate readings without introducing a significant impedance.These sensors have galvanic isolation and a wide frequency response; however, they do not allow the measurement of DC currents [3,4,6].Hall effect sensors used for current measurement consist in semiconductor materials that generate a voltage proportional to the current passing through a conductor when exposed to a magnetic field [7].
Sensors 2024, 24, 3047 3 of 12 In Section 2.1, the proposed conditioning circuit enabling the MR element to function as a current sensor is analyzed.The proposed thermal compensation method is explained in Section 2.2.Section 3 outlines the experimental results, including the validation of the electronic interface, measurements of the sensitivity temperature coefficient without compensation, and the outcomes when the proposed compensation is implemented.In Section 4, a brief discussion takes place, while in Section 5, conclusions are drawn.

MR-Shunt Definition and Thermal Characterization
In this paper, tunnel magnetoresistance (TMR) effect-based sensing elements, both arranged in a Wheatstone bridge configuration and single element, were used.Sensors micro-fabrication was carried out at the INESC-MN facilities in Lisbon.In the case of the magnetoresistive bridge, named TMR46, each element was made up of the following layers (thicknesses in nm): Si/100 SiO 2 /5 Ta/ 15  Figure 1 shows the layout of the tracks and their implementation for the single element (LCEL1).In the case of the magnetoresistive bridge, the current passes through a U-shaped copper bar located at the bottom of the PCB, while in the case of the single element, a properly designed single track on the PCB was used.
tronic interface, measurements of the sensitivity temperature coefficient without com sation, and the outcomes when the proposed compensation is implemented.In Secti a brief discussion takes place, while in Section 5, conclusions are drawn.

MR-Shunt Definition and Thermal Characterization
In this paper, tunnel magnetoresistance (TMR) effect-based sensing elements, arranged in a Wheatstone bridge configuration and single element, were used.Figure 1 shows the layout of the tracks and their implementation for the single ment (LCEL1).In the case of the magnetoresistive bridge, the current passes through shaped copper bar located at the bottom of the PCB, while in the case of the single elem a properly designed single track on the PCB was used.In order to be able to use the TMR sensors configured in a Wheatstone bridge a MR-shunt, a circuit was devised that allows the rest of the elements to be cancelled circuit is shown in Figure 2a, where sensor elements R2, R3, and R4 are eliminated (in particular case), leaving only element R1 as the active element.By action of operat amplifiers OA1 and OA2, current through R2 and R3 elements is zero and, therefore, zero through R4.As a consequence, only element R1 of the WB is active and constant rent biased by Iref.The equivalent circuit is shown in Figure 2b, where the active ele is named, in a general case, Rs (s = 1 in this particular case).In order to be able to use the TMR sensors configured in a Wheatstone bridge as an MR-shunt, a circuit was devised that allows the rest of the elements to be cancelled.The circuit is shown in Figure 2a, where sensor elements R 2 , R 3 , and R 4 are eliminated (in this particular case), leaving only element R 1 as the active element.By action of operational amplifiers OA 1 and OA 2 , current through R 2 and R 3 elements is zero and, therefore, also zero through R 4 .As a consequence, only element R 1 of the WB is active and constant current biased by I ref .The equivalent circuit is shown in Figure 2b, where the active element is named, in a general case, R s (s = 1 in this particular case).

MR-Shunt Definition and Its Electronic Interface
In Figure 2b, the action of an external magnetic field H, generated by the current i to be measured, according to the MR effect [25][26][27], results in a magnetic resistance change (ΔRs) proportional to the applied magnetic field within its linear range and, therefore, proportional to the current to be measured: with  Ω (in Ω/A) being the resistive sensitivity of the MR-shunt and Ros the sensor resistance at zero input current.
To convert the change of resistance into voltage, the MR-shunt Rs in Figure 2b is biased at a constant current Iref and the voltage v measured: with S being the sensor voltage sensitivity (in V/A), which depends on the sensor type and the supplied current Iref, and Voff the voltage at zero input current, The conditioning circuit used for the MR-shunt is shown in Figure 3.It is based on a voltage-to-current converter (OA3 and OA4) that provides the reference current Iref and a current mirror (REF200 from Texas Instruments, Dallas, TX, USA) that replicates this current in the MR-shunt.The current Iref is set by the voltage reference Z1 (2.5 V) and P1 that adjusts it to the desired value (e.g., 1 mA).The differential voltage vd in Figure 3, by considering Rs of (1), is: For zero current i (i.e., Δ  = 0), P2 allows adjusting the voltage   = −  ⋅  2 in Figure 3 to the offset voltage (Voff) of Equation (4), in such a way that vd is equal to zero.Therefore, after offset adjustment:

MR-Shunt Definition and Its Electronic Interface
In Figure 2b, the action of an external magnetic field H, generated by the current i to be measured, according to the MR effect [25][26][27], results in a magnetic resistance change (∆R s ) proportional to the applied magnetic field within its linear range and, therefore, proportional to the current to be measured: with S Ω (in Ω/A) being the resistive sensitivity of the MR-shunt and R os the sensor resistance at zero input current.
To convert the change of resistance into voltage, the MR-shunt R s in Figure 2b is biased at a constant current I ref and the voltage v measured: with S being the sensor voltage sensitivity (in V/A), which depends on the sensor type and the supplied current and V off the voltage at zero input current, The conditioning circuit used for the MR-shunt is shown in Figure 3.It is based on a voltage-to-current converter (OA 3 and OA 4 ) that provides the reference current I ref and a current mirror (REF200 from Texas Instruments, Dallas, TX, USA) that replicates this current in the MR-shunt.The current I ref is set by the voltage reference Z 1 (2.5 V) and P 1 that adjusts it to the desired value (e.g., 1 mA).The differential voltage v d in Figure 3, by considering R s of (1), is: the R6-R7-C1-C2-C3 network.This prevents any RFI content from contributing to an offset voltage at the output of the instrumentation amplifier that will not be eliminated by subsequent low-pass filtering [28].In this design, there is a cutoff frequency for the differential mode of 2 kHz ( , = 1 2(2 1 + 3 ) 6 ) and for the common mode of 50 kHz ( , = 1 2 6  3 ).
The resulting signal is then conditioned by an instrumentation amplifier (IA), with gain G, and a non-inverter amplifier (OA5) to obtain the output voltage vo.

MR-Shunt Compensation Method
The compensation method described below is based on imposing a zero-temperature coefficient to the variable to compensate, which gives a design condition for the compensation circuit.This technique has been successfully applied in force, pressure, or magnetic field sensor bridges, as well as in the design of precision voltage references [29][30][31].
If a thermal dependence of the sensitivity S is considered in the form: where So and TCS are, respectively, the sensor sensitivity and its temperature coefficient at temperature To, then Equation ( 6) can be written as: so that the temperature coefficient of vd at T = To is: To compensate for the vd variation in temperature, a temperature-variable resistor RT is added in the gain of the non-inverting amplifier (Figure 3).In this way, its output voltage vo will be given by:   =  , ⋅  ⋅   (10) where: By applying natural logarithms in Equation (10) and then differentiating, it is possible to obtain the expression: For zero current i (i.e., ∆R s = 0), P 2 allows adjusting the voltage V p = −I re f • P 2 in Figure 3 to the offset voltage (V off ) of Equation ( 4), in such a way that v d is equal to zero.Therefore, after offset adjustment: Next, the differential voltage v d is Radio Frequency Interference (RFI)-filtered using the R 6 -R 7 -C 1 -C 2 -C 3 network.This prevents any RFI content from contributing to an offset voltage at the output of the instrumentation amplifier that will not be eliminated by subsequent low-pass filtering [28].In this design, there is a cutoff frequency for the differential mode of 2 kHz ( f c,dm = ) and for the common mode of 50 kHz ( f c,cm = 1 2πR 6 C 3 ).The resulting signal is then conditioned by an instrumentation amplifier (IA), with gain G, and a non-inverter amplifier (OA 5 ) to obtain the output voltage v o .

MR-Shunt Compensation Method
The compensation method described below is based on imposing a zero-temperature coefficient to the variable to compensate, which gives a design condition for the compensation circuit.This technique has been successfully applied in force, pressure, or magnetic field sensor bridges, as well as in the design of precision voltage references [29][30][31].
If a thermal dependence of the sensitivity S is considered in the form: where S o and TCS are, respectively, the sensor sensitivity and its temperature coefficient at temperature T o , then Equation ( 6) can be written as: so that the temperature coefficient of v d at T = T o is: Sensors 2024, 24, 3047 6 of 12 To compensate for the v d variation in temperature, a temperature-variable resistor R T is added in the gain of the non-inverting amplifier (Figure 3).In this way, its output voltage v o will be given by: where: By applying natural logarithms in Equation (10) and then differentiating, it is possible to obtain the expression: with G being constant with temperature.
If derivatives are now calculated with respect to temperature, to achieve a TCv o = 0 at temperature T o , the following condition must be met: From Equation (11), it is possible to obtain, for TCG n,inv : Thus, from Equation ( 13), a specific value for resistance R 9 is obtained at a given compensation temperature: To obtain a physically feasible value of R 9 , it will be necessary that TCR T > TCS.

Experimental Results
To validate the proposed electronic interface and the effectiveness of the compensation method, two MR-shunt elements were subjected to an i current sweep.The first one was integrated into a WB with the connections indicated in Figure 2a and the second element implemented autonomously.

Electronic Interface Validation
The MR-shunt element was biased at a constant current value of I ref = 1 mA with a +2.5 V reference voltage (LM4040DIZ from Texas Instruments, Dallas, TX, USA) and adjusting potentiometer P 1 .By means of a transconductance amplifier (PCS-2B from Krohn-Hite Corporation, Brockton, MA, USA), a current sweep from −10 A to +10 A was generated in a PC-controlled manner and the MR-shunt voltage v d was acquired using a multimeter (K2000 from Keithley, Solon, OH, USA).Potentiometer P 2 was adjusted to achieve zero v d output at zero current i. Figure 4 shows the experimental responses of the v d voltage corresponding to the MR-shunt element embedded in the Wheatstone bridge (Figure 4a) and the single element (Figure 4b) at a temperature T = 20 • C. justing potentiometer P1.By means of a transconductance amplifier (PCS-2B from Kr Hite Corporation, Brockton, MA, USA), a current sweep from −10 A to +10 A was g ated in a PC-controlled manner and the MR-shunt voltage vd was acquired using a trolled multimeter (K2000 from Keithley, Solon, OH, USA).Potentiometer P2 was adju to achieve zero vd output at zero current i. Figure 4 shows the experimental respons the vd voltage corresponding to the MR-shunt element embedded in the Wheats bridge (Figure 4a) and the single element (Figure 4b) at a temperature T = 20 °C.In Figure 4, a high degree of linearity is obtained in both the MR-shunt element embedded in the Wheatstone bridge (TMR46) and the single element (LCEL1).However, the linearity is slightly higher in the LCEL1 element than in the TMR46, probably due to a residual influence of the other three MR elements present in the Wheatstone bridge configuration.In a potential application, the practical linear range of the embedded element should be reduced and the use of the isolated MR element would be even more advisable.Moreover, a higher sensitivity for the LCEL1 element was also observed than that for the TMR46 due to its particular manufacturing structures.

Sensitivity Temperature Coefficients without Compensation
Similar to the methodology employed in the previous section, voltage v d was measured in response to the i current sweep at different temperatures by placing the MR element within a climatic chamber (CH600 VT from Angelantoni, Massa Martana, Italy).Thermal analysis was performed in the temperature range of −20 to 60 • C. The current sensitivity S for voltage v d at each temperature was subsequently analyzed through linear regression, similar to the way as shown in Figure 4.The change in S with temperature is shown in Figure 5.In Figure 4, a high degree of linearity is obtained in both the MR-shunt element embedded in the Wheatstone bridge (TMR46) and the single element (LCEL1).However, the linearity is slightly higher in the LCEL1 element than in the TMR46, probably due to a residual influence of the other three MR elements present in the Wheatstone bridge configuration.In a potential application, the practical linear range of the embedded element should be reduced and the use of the isolated MR element would be even more advisable.Moreover, a higher sensitivity for the LCEL1 element was also observed than that for the TMR46 due to its particular manufacturing structures.

Sensitivity Temperature Coefficients without Compensation
Similar to the methodology employed in the previous section, voltage vd was measured in response to the i current sweep at different temperatures by placing the MR element within a climatic chamber (CH600 VT from Angelantoni, Massa Martana, Italy).Thermal analysis was performed in the temperature range of −20 to 60 °C.The current sensitivity S for voltage vd at each temperature was subsequently analyzed through linear regression, similar to the way as shown in Figure 4.The change in S with temperature is shown in Figure 5.
Temperature dependence of the current sensitivity S shows a good linearity with a slope m of 0.0082 mV/A°C for the TMR46 and 0.0333 mV/A°C for the LCEL1, which is equivalent at To = 20 °C to a TCS of 0.3482%/°C and 0.4743%/°C, respectively.Moreover, a higher temperature dependence and degree of linearity are shown for the single element LCEL1, according to its greater sensitivity and better linearity (see Figure 4b).

Sensitivity Temperature Coefficients with Compensation
Once thermal characterization of the two MR elements had been carried out, the aim was to minimize the thermal dependence of their electronic interface (voltage vo in Figure 3).The objective was to decrease the gain of the non-inverting stage as the temperature rises, thus compensating for the temperature-induced increase in sensitivity of the MR sensor.In this way, resistance RT must be a temperature sensor with positive TC, and the Temperature dependence of the current sensitivity S shows a good linearity with a slope m of 0.0082 mV/A • C for the TMR46 and 0.0333 mV/A • C for the LCEL1, which is equivalent at T o = 20 • C to a TCS of 0.3482%/ • C and 0.4743%/ • C, respectively.Moreover, a higher temperature dependence and degree of linearity are shown for the single element LCEL1, according to its greater sensitivity and better linearity (see Figure 4b).

Sensitivity Temperature Coefficients with Compensation
Once thermal characterization of the two MR elements had been carried out, the aim was to minimize the thermal dependence of their electronic interface (voltage v o in Figure 3).The objective was to decrease the gain of the non-inverting stage as the temperature rises, thus compensating for the temperature-induced increase in sensitivity of the MR sensor.In this way, resistance R T must be a temperature sensor with positive TC, and the value of R 9 will be determined by Equation ( 15) obtained in the compensation method (Section 2.2).
For R T , four possible temperature sensors were considered and thermally characterized.Three of them were resistive temperature detectors (RTDs), two platinum-based (Pt100 and Pt1k), and one Ruthenium-based (Ru), while the fourth was a silicon-based temperature sensor (the KTY81-122 model [32,33] from NXP Semiconductors, Eindhoven, The Netherlands).Experimental measurements for each sensor provided the temperature coefficients outlined in Table 1.
Table 1.Temperature coefficients in %/ • C of the three temperature sensors used for compensation.

Temperature Sensor
According to Equation (15), suitable resistance values for R 9 were obtained using the Pt1k and KTY81-122 sensors for the embedded element TMR46 and the KTY81-122 sensor for the single element LCEL1.
In a similar way to measurement of the sensing elements, the voltage v o measurements were carried out at the temperatures outlined in Section 3.2, performing the current sweep detailed in Section 3.1.
Figures 6 and 7 show the values of the current sensitivity S vo of the voltage v o at the output of the electronic interface at different temperatures for the TMR46 and the LCEL1 MR-shunts, respectively, after temperature compensation.The main results are summarized in Table 2, where TC wnc denotes the temperature coefficients obtained without compensation (Section 3.2) and TC wc with compensation (Table 2).A figure of merit that reflects the effectiveness of the thermal compensation performed is the percentage in reduction R experienced in the temperature coefficient before and after compensation, defined as: Sensors 2024, 24, 3047 As summarized in Table 2, it was possible to reduce the initial temperature coefficients of the MR-shunt elements, achieving high reduction coefficients in all the cases tested, especially when the silicon-based temperature sensor was used.
A figure of merit that reflects the effectiveness of the thermal compensation performed is the percentage in reduction R experienced in the temperature coefficient before and after compensation, defined as: As summarized in Table 2, it was possible to reduce the initial temperature coefficients of the MR-shunt elements, achieving high reduction coefficients in all the cases tested, especially when the silicon-based temperature sensor was used.

Discussion
The temperature coefficient of MR-shunt elements can be hardware-compensated by the use of a suitable conditioning circuit (Figure 3) and a specific temperature sensor (compensator).The proposed compensation method is based on the variation of voltage gain with temperature and obtains a resistance whose realizability depends on the relationship between temperature coefficients of the compensator and the MR-shunt element (Equation (15)).Therefore, it is convenient to use compensators with high temperature coefficients, like those implemented from silicon, such as the one described in the work [32] (0.790%/°C) or the type of RTDs based on Pt (0.353%/°C).Regarding these two compensators, Figures 6 and 7 show a more optimal thermal compensation when using the siliconbased compensator.Higher TCRT values result in a resistance R9 that is less sensitive to changes in the temperature coefficient of the compensator, particularly away from negative values and the point of indetermination, thus achieving better compensation.RTDs based on Ni with TC values around 0.618%/°C [34,35] or linear thermistors [36] would also be suitable but have not been tested in this work.
In the case of the MR-element embedded in the Wheatstone bridge, the other three MR elements present in it affect the results.The magnetic behavior of an MR element is

Discussion
The temperature coefficient of MR-shunt elements can be hardware-compensated by the use of a suitable conditioning circuit (Figure 3) and a specific temperature sensor (compensator).The proposed compensation method is based on the variation of voltage gain with temperature and obtains a resistance whose realizability depends on the relationship between temperature coefficients of the compensator and the MR-shunt element (Equation ( 15)).Therefore, it is convenient to use compensators with high temperature coefficients, like those implemented from silicon, such as the one described in the work [32] (0.790%/ • C) or the type of RTDs based on Pt (0.353%/ • C).Regarding these two compensators, Figures 6  and 7 show a more optimal thermal compensation when using the silicon-based compensator.Higher TCR T values result in a resistance R 9 that is less sensitive to changes in the temperature coefficient of the compensator, particularly away from negative values and the point of indetermination, thus achieving better compensation.RTDs based on Ni with TC values around 0.618%/ • C [34,35] or linear thermistors [36] would also be suitable but have not been tested in this work.
In the case of the MR-element embedded in the Wheatstone bridge, the other three MR elements present in it affect the results.The magnetic behavior of an MR element is not the same when it is joined to the other three by means of a Wheatstone bridge connection than when it is alone.In Figure 2, as was previously explained, the operational amplifiers OA 1 and OA 2 establish a zero-voltage difference in the adjacent elements R 2 and R 3 , blocking the current I ref through them, and thus preventing their polarization.However, in real operational amplifiers, an offset voltage exists that gives a non-zero voltage difference between their input terminals.Consequently, the voltage difference in R 2 and R 3 differs from zero in this offset voltage, thus allowing a residual polarization in these components.This residual polarization is probably the cause of less linearity of this configuration, as evidenced by the experimental data presented in Figures 4a and 5a.In the present work, ultralow offset voltage operational amplifiers OA 1 and OA 2 were selected to minimize the residual polarization of R 2 and R 3 elements to a level less than 0.1 µA.Figures 4a and 5a depict how residual polarization impacts the linear behavior of the embedded MR element and its temperature sensitivity.The use of a single MR element enhances the linearity of its behavior, as evidenced by the results presented in Figures 4b and 5b.
Compensations of current sensors in Wheatstone bridge configuration based on spinvalve technology were presented in [37][38][39].For these cases, a compensator based on an Ru RTD sensor was integrated into the same substrate as the sensor bridge.In that situation, the bridge supply current varied with temperature.In the design presented, it is the gain of a voltage amplifier that changes with temperature and the TC of an Ru-based compensator was not sufficient to satisfy Equation (15).It would be highly desirable to have MR-shunt elements and Ru-based compensators sharing the same substrate to enhance thermal coupling between them, thereby enabling better thermal compensation using methods as described in [37][38][39].

Conclusions
A magnetoresistance-based current sensor has been presented that, on a practical level, offers the simplicity of a shunt resistor, while avoiding drawbacks such as galvanic isolation and self-heating issues.In this way, the concept of a magnetoresistive shunt (MR-shunt) is presented.The design replaces the conventional Wheatstone bridge structure used in magnetoresistive sensors with just a single MR element.This not only simplifies the microelectronic processes but also reduces the layout complexity of connections.Furthermore, the proposed electronic system includes compensation for the sensitivity thermal drift commonly associated with these sensors.
For the analyzed sensors, linear response behavior was obtained in the measurement range for currents between −10 and 10 A. Furthermore, by adding an external resistive temperature sensor (Pt1k or KTY) and with the proposed circuitry, a strong reduction in thermal dependence of the sensitivity was achieved (R > 94%, Table 2).

Figure 2 .
Figure 2. (a) Electronic circuitry to reduce an MR Wheatstone bridge sensor to an MR-shunt and (b) its equivalent circuit.

Figure 2 .
Figure 2. (a) Electronic circuitry to reduce an MR Wheatstone bridge sensor to an MR-shunt and (b) its equivalent circuit.

Figure 4 .Figure 4 .
Figure 4. Voltage difference vd corresponding to a current sweep from −10 A to +10 A. (a) M ment embedded in a Wheatstone bridge (TMR46) and (b) stand-alone element (LCEL1), T = 2 Figure 4. Voltage difference v d corresponding to a current sweep from −10 A to +10 A. (a) MR element embedded in a Wheatstone bridge (TMR46) and (b) stand-alone element (LCEL1), T = 20 • C.

Figure 5 .
Figure 5. Temperature dependence of the current sensitivity S corresponding to: (a) MR element embedded in a Wheatstone bridge (TMR46) and (b) single element (LCEL1).

Figure 5 .
Figure 5. Temperature dependence of the current sensitivity S corresponding to: (a) MR element embedded in a Wheatstone bridge (TMR46) and (b) single element (LCEL1).

Figure 6 .
Figure 6.Temperature dependence of the current sensitivity Svo of the voltage vo at the output of the electronic interface corresponding to the MR element embedded in a Wheatstone bridge (TMR46) using the temperature sensors (a) RTD-Pt1k and (b) silicon-based KTY81-122.

Figure 6 .
Figure 6.Temperature dependence of the current sensitivity S vo of the voltage v o at the output of the electronic interface corresponding to the MR element embedded in a Wheatstone bridge (TMR46) using the temperature sensors (a) RTD-Pt1k and (b) silicon-based KTY81-122.

Figure 7 .
Figure 7. Temperature dependence of the current sensitivity Svo of the voltage vo at the output of the electronic interface corresponding to the stand-alone element (LCEL1) using the silicon-based temperature sensor KTY81-122.

Figure 7 .
Figure 7. Temperature dependence of the current sensitivity S vo of the voltage v o at the output of the electronic interface corresponding to the stand-alone element (LCEL1) using the silicon-based temperature sensor KTY81-122.

Table 2 .
Temperature coefficients in %/ • C without and with compensation, and the percentage of reduction R (%).

Table 2 .
Temperature coefficients in %/°C without and with compensation, and the percentage of reduction R (%).